US president-elect Donald Trump has released what he says is a "very nice" letter from Russia's president, Vladimir Putin, calling for a thaw in ties between the rival powers.

Trump's transition team said late on Friday that the president-elect received the letter from Putin urging him to act "in a constructive and pragmatic manner" to "restore the framework of bilateral cooperation".

The letter, dated December 15, also noted that serious global and regional challenges "show that the relations between Russia and the US remain an important factor in ensuring stability and security in the modern world".

In response, Trump agreed with Putin, adding that he hopes "we do not have to travel an alternate path".

Putin spokesman Dmitry Peskov confirmed on Saturday that Putin sent the letter, "voicing hope for an improvement of bilateral ties", according to the Interfax news agency.

The exchange comes on the heels of comments by Trump and Putin about the need to strengthen their countries' nuclear arsenals.

Trump tweeted on Thursday that the US should "greatly strengthen and expand its nuclear capability". He said the nation must do so until the rest of the world - as he put it - "comes to its senses" regarding nuclear weapons.

Those comments echoed an earlier statement by Putin, who said that strengthening his country's nuclear capabilities should be a chief military objective in the coming year.

Putin said he saw "nothing unusual" in Trump's pledge to strengthen the US nuclear forces, and claimed that his country's military is stronger than that of any potential aggressor, but acknowledged that the US military is bigger.

He also cast the modernisation of Russia's nuclear arsenal as a necessary response to a US missile defence system.

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The US currently has an estimated arsenal of about 7,000 nuclear warheads, second only to Russia, which has a few hundred more.

During the next decade, US ballistic missile submarines, bombers, and land-based missiles - the three legs of the nuclear triad - are expected to reach the end of their useful lives.

Maintaining and modernising the arsenal is expected to cost at about $1 trillion over 30 years.

Source: Al Jazeera and news agencies